Multi-symplectic formulation of near-local Hamiltonian balanced models

DOI10.1098/rspa.2011.0147zbMath1243.86004OpenAlexW2113297231MaRDI QIDQ2901813

Peter E. Hydon, Sylvain Delahaies

Publication date: 31 July 2012

Published in: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1098/rspa.2011.0147

zbMATH Keywords

balanced modelsmulti-symplectic systemsemigeostrophic theory

Mathematics Subject Classification ID

Hydrology, hydrography, oceanography (86A05) Symplectic geometry, contact geometry (53D99) PDEs in connection with geophysics (35Q86)

Cites Work

• Dirac-bracket approach to nearly geostrophic Hamiltonian balanced models
• Extended-geostrophic Hamiltonian models for rotating shallow water motion
• Symmetry group analysis of the shallow water and semi-geostrophic equations
• Multisymplectic structures and the variational bicomplex
• Practical use of Hamilton's principle
• New equations for nearly geostrophic flow
• Weak Existence for the Semigeostrophic Equations Formulated as a Coupled Monge--Ampère/Transport Problem
• A geometric formulation of the conservation of wave action and its implications for signature and the classification of instabilities
• The mathematical structure of theories of semigeostrophic type
• Vorticity and symplecticity in Lagrangian fluid dynamics
• Planetary semi-geostrophic equations derived from Hamilton's principle
• Hyper-Kähler geometry and semi-geostrophic theory
• Multisymplectic formulation of fluid dynamics using the inverse map
• Numerical methods for Hamiltonian PDEs

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